Ghee is a type of clarified butter. Based on the nutty flavor of most I have purchased, I would imagine it is cooked more (less water). Also, I have seen that the milk used may be allowed to sour slightly for ghee.

To my knowledge ghee is clarified butter. Flavors can vary, I'm guessing it has to do with the milk in which the butter is made from. But clarified butter's flavor can vary from batch to batch depending on how far or how much it is simmered. Some chefs I've work for prefered a brown-er flavor than just to the point of liquefication and clarification.

Ghee is actually from cultured milk that has been soured. In traditional Ghee preparation, the butter is melted and once it has separated over heat, the milk solids are allowed to brown very gently, this gives ghee its toasted quality, similar to browned butter. Clarified butter is simply melted butter that has had its milk solids removed.